Hybrid system stability and robustness verification using linear matrix inequalities. (English) Zbl 1017.93027

The authors discuss the exponential stability and robustness of hybrid systems. Stability conditions are given. The authors have shown how the Lyapunov approach can be used to guarantee stability despite the presence of model uncertainties. Many examples are given to illustrate the theory.


93B12 Variable structure systems
93D20 Asymptotic stability in control theory
15A39 Linear inequalities of matrices
93D09 Robust stability


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[1] BALAKRISHNAN, J. May 1996. ”Control system design using multiple models, switching, and tuning”. May, USA: University of Yale. PhD dissertation, 1996
[2] BOYD S., Linear Matrix Inequalities in System and Control Theory (1994) · Zbl 0816.93004
[3] BROGAN W. L., Modern Control Theory pp 121– (1991) · Zbl 0747.93001
[4] DRIANKOV D., An Introduction in Fuzzy Control (1993) · Zbl 0789.93088
[5] DOI: 10.1109/91.919252
[6] DOI: 10.1109/91.298450
[7] DOI: 10.4173/mic.1992.1.3
[8] DOI: 10.1080/00207179308923046 · Zbl 0787.93004
[9] DOI: 10.1109/91.855918
[10] DOI: 10.1109/91.811241
[11] KIRIAKIDIS, K. 1998. ”Analytical methods for stability and synthesis of control systems associated with fuzzy logic”. Brooklyn. New York, USA: Polytechnic University. Department of Mechanical Engineering. PhD Dissertation
[12] DOI: 10.1109/9.554398 · Zbl 0869.93025
[13] DOI: 10.1109/9.898709 · Zbl 0992.93035
[14] DOI: 10.1080/00207170010023791 · Zbl 1015.93059
[15] PAGÈS O., Application à un axe robotisé (2001)
[16] PAGÈS, O., MOUILLE, P. and CARON, B. Multi-model control by applying a symbolic fuzzy switcher. Proceedings of the Conference on Control Systems Design. June, Slovak Republic. pp.477–482. Bratislava CSD 2000
[17] PAGÈS, O., MOUILLE, P. and CARON, B. Two approaches of the multi-model control. Real-time implementation for a wrist of a robot. Proceedings of Mechatronics 2000. Darmstadt. Germany. September. Volume 2, pp.483–488.
[18] PAGÈS, U., MOUILLE, P. and CARON, B. Multi-controllers approach with local fuzzy controllers. Real-time implementation for a wrist of a robot. Proceedings of the European Centrol Conference Porto. September, Portugal. pp.226–231.
[19] DOI: 10.1016/0167-6911(87)90102-2 · Zbl 0618.93056
[20] DOI: 10.1109/72.165588
[21] SLOTINE J. J. E., Applied Nonlinear Control pp 339– (1991) · Zbl 0753.93036
[22] DOI: 10.1016/0165-0114(92)90113-I · Zbl 0758.93042
[23] VIDYASAGAR M., Nonlinear Systems Analysis pp 6–, 2. ed. (1993)
[24] DOI: 10.1109/91.481841
[25] DOI: 10.1016/S0165-0114(99)00056-1 · Zbl 0988.93046
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